Calculation of strayfields near grain edges in permanent magnet material

The internal strayfields near the edges of permanent magnetic grains are calculated. A numerical algorithm has been developed to consider the modification of the strayfield resulting from the rotation of the magnetization from the easy axis in external and internal fields. Anisotropy constants of higher order are considered. The results are applied to Nd₂Fe₁₄B. The ratio between strayfield strength and saturation magnetization defines a theoretical local demagnetizing factor which is comparable with the effective demagnetizing factor used to describe the temperature dependence of coercivity. The effect of strayfields on the coercive field and its angular dependence is discussed.     

磁性纳米颗粒系统偶极相互作用的Monte Carlo研究

采用局域Monte Carlo方法模拟不同易轴分布的简单立方排列单分散单畴Fe纳米颗粒系统的ZFC-FC曲线及磁滞回线.结果表明：随着偶极相互作用的增强，系统的阻塞温度T_B逐渐增大，且ZFC曲线的峰变宽.说明偶极相互作用使得系统的有效能垒提高，分布宽度增加.研究FC曲线磁化强度的倒数与温度关系，发现偶极相互作用系统中存在反铁磁有序.系统的阻塞态及超顺磁态的磁滞回线表明，极低低温下，随着偶极相互作用的增强，系统的矫顽力和剩磁减小，偶极相互作用阻碍系统的磁化；系统处于超顺磁态，各向异性作用及偶极相互作用使得系统的磁化曲线偏离Langevin曲线且偶极相互作用展现出退磁相互作用效应.偶极相互作用增强，系统磁化曲线与Langevin曲线偏差量的最大值向低场移动.在偶极相互作用下，易轴与外场夹角为45°的磁性纳米颗粒系统的平均有效能垒和有效能垒分布宽度较易轴随机分布系统的大.     

Non-equilibrium effects in the magnetic behavior of Co3O4 nanoparticles

We report detailed studies of the non-equilibrium magnetic behavior of antiferromagnetic Co₃O₄ nanoparticles. The temperature and field dependence of magnetization, wait time dependence of magnetic relaxation (aging), memory effects, and temperature dependence of specific heat have been investigated to understand the magnetic behavior of these particles. We find that the system shows some features that are characteristic of nanoparticle magnetism such as bifurcation of field-cooled (FC) and zero-field-cooled (ZFC) susceptibilities and a slow relaxation of magnetization. However, strangely, the temperature at which the ZFC magnetization peaks coincides with the bifurcation temperature and does not shift on application of magnetic fields up to 1 kOe, unlike most other nanoparticle systems. Aging effects in these particles are negligible in both FC and ZFC protocols, and memory effects are present only in the FC protocol. We show that Co₃O₄ nanoparticles constitute a unique antiferromagnetic system which enters into a blocked state above the average Néel temperature.     

New micromagnetic states of magnetically soft nanoparticles with a nearly cubic shape

The ground state of nonellipsoidal particles can be inhomogeneous due to the effect of a demagnetizing field. The approach proposed here for studying such particles is based on the combination of symmetry analysis and perturbation theory. The general formulation of this approach, which makes it possible to analyze weakly inhomogeneous states for particles with a complex shape, is considered. The ground state of cubic particles of magnetically soft materials is calculated analytically, and the effect of small strains of cubic particles on the magnetization distribution in the particles is investigated. It is shown for the example of magnetically soft cubic particles that even a small deviation of the particle shape from symmetrical may result in the realization of a special magnetic state in such particles, in which the symmetry in the magnetization distribution is lower than the particle symmetry. A change in the parameters of a particle can substantially modify its magnetic properties and may even induce a phase transition to a state with a different symmetry.     

Temperature magnetic hysteresis of precipitation-hardened alloys

The temperature variation of the residual magnetization of the precipitation-hardened alloys Alnico and Ticonal is considered. The temperature hysteresis of the magnetization due to the irreversible magnetization reversal of single-domain particles is related to the temperature dependence of the anisotropy constant and the value of the demagnetizing field. The magnetic state of the matrix phase affects the irreversible process of magnetization reversal of the strongly magnetic particles. The residual magnetization may include a component due to superparamagnetic inclusions in the matrix phase, giving a contribution to the temperature hysteresis in heating-cooling cycles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 26–32, October, 1976.     

Anomalous magnetic behavior of CuO nanoparticles

We report studies on temperature, field and time dependence of magnetization on cupric oxide nanoparticles of sizes 9 nm, 13 nm and 16 nm. The nanoparticles show unusual features in comparison to other antiferromagnetic nanoparticle systems. The field cooled (FC) and zero field cooled (ZFC) magnetization curves bifurcate well above the Néel temperature and the usual peak in the ZFC magnetization curve is absent. The system does not show any memory effects which is in sharp contrast to the usual behavior shown by other antiferromagnetic nanoparticles. It turns out that the non-equilibrium behavior of CuO nanoparticles is very strange and is neither superparamagnetic nor spin glass like.     

Field induced spin reorientation transition in epitaxial La0.5Sr0.5CoO3 films

Strained epitaxial La_0.5Sr_0.5CoO₃ films are grown on LaAlO₃ substrate. Structural, electrical, and magnetic measurements were carried out. Out of plane lattice parameter of the film undergoes compressive strain and the coercivity is enhanced. The zero field cooled (ZFC) magnetization curve for a field applied parallel to the film plane shows a jump, which suggests a spin reorientation transition (SRT), while ZFC magnetization for a field applied perpendicular to the film plane is featureless. This jump in magnetization is shifted to higher temperatures when the magnetic field is reduced. The SRT is attributed to the strain in the film.     

Magnetization processes in nanocrystalline gadolinium

The thermal decline in magnetization, M(T), at fixed magnetic field (H) under 'zero-field-cooled' (ZFC) and 'field-cooled' (FC) conditions, the time evolution of ZFC magnetization, M(ZFC)(t), at fixed temperature and field, M(H) hysteresis loops/isotherms, and ac susceptibility have been measured on polycrystalline Gd samples with average grain sizes of d = 12 and 18 nm. The irreversibility in magnetization, M(irr), occurring below a characteristic temperature that reduces with increasing H, is completely suppressed above a grain-size-dependent threshold field, H*. At low fields (H ≤ 100 Oe), M(irr)(T), like the coercive field, H(c)(T), exhibits a minimum at ～16 K and a broad peak at ～50 K before going to zero at T ? T(C) (Curie temperature). At fixed temperature (T < T(C)) and field (H ? H*), where M(irr) is finite, M(ZFC) has a logarithmic dependence on time. The magnetic viscosity (S) at H = 1 Oe and T ≤ 290 K is independent of the measurement time above ～2 ms but for t < 2 ms it is strongly time-dependent. S(T) peaks at T ? T(C) for H = 1 Oe. A magnetic field reduces the peak height and shifts the peak in S(T) to lower temperatures. All the above observations are put on a consistent theoretical footing within the framework of a model in which the intra-grain magnetizations overcome the energy barriers (brought about by the intra-grain and grain-boundary/interfacial magnetic anisotropies) by the thermal activation process. These field- and temperature-dependent energy barriers, that separate the high-energy metastable (ZFC) state from the stable minimum-energy (FC) state, are independent of time for t ? 2 ms and have a very broad distribution. We show that the shape anisotropy plays a decisive role in the magnetization reversal process, and that the magnetocrystalline and magnetostatic fluctuations, prevalent in the grain-boundary and interfacial regions, govern the approach-to-saturation of magnetization in nanocrystalline Gd.     

Magnetic Behaviour and Heating Effect of Fe3O4 Ferrofluids Composed of Monodisperse Nanoparticles

Fe3O4 ferrofluids containing monodisperse Fe3O4 nanoparticles with different diameters of 8, 12, 16 and 18nm are prepared by using high-temperature solution phase reaction. The particles have single crystal structures with narrow size distributions. At room temperature, the 8-nm ferrofluid shows superparamagnetic behaviour, whereas the others display hysteresis properties and the coercivity increases with the increasing particle size. The spin glass-like behaviour and cusps near 190K are observed on all ferrofluids according to the temperature variation of field-cooled （FC） and zero-field-cooled （ZFC） magnetization measurements. The cusps are found to be associated with the freezing point of the solvent. As a comparison, the ferrofluids are dried and the FC and ZFC magnetization curves of powdery samples are also investigated. It is found that the blocking temperatures for the powdery samples are higher than those for their corresponding ferrofluids. Moreover, the size dependent heating effect of the ferrofluids is also investigated in ac magnetic field with a frequency of 55 kHz and amplitude of 200 Oe.     

Critical magnetization and hysteresis of nanogranular films with perpendicular anisotropy

The magnetic-field dependences of the stability boundaries of the nonequilibrium magnetic states that exist in a nanogranular film with perpendicular anisotropy in tilted magnetic fields are theoretically described, and the corresponding critical magnetization is calculated. The field dependences of the critical magnetization of the film are analyzed at various ratios of the anisotropy field of particles to the maximum possible demagnetizing field of the film. In a tilted magnetic field, the magnetization reversal curves, which include hysteresis loops, are shown to consist of segments of the following three types: equilibrium stable magnetization, nonequilibrium stable magnetization, and critical type of magnetization.     

Evidence of Verwey transition in iron- and iron oxide-encapsulated carbon nanotubes

Magnetization measurements in two different samples of iron- and iron oxide-encapsulated carbon nanotubes are presented. The samples showed coercivity smaller than 1 kOe. The dependence of the coercivity with the temperature has an abrupt change at temperatures close to 125 K. In this temperature the ZFC and FC magnetization curves also present an abrupt change. This effect is attributed to a Verwey transition.     

Investigation of the static and dynamic magnetic properties of CoFe2O4 nanoparticles

We have investigated the magnetic behavior of cobalt ferrite nanoparticles with a mean diameter of 7.2 nm. AC susceptibility of colloidal cobalt ferrite nanoparticles was measured as a function of temperature T from 2 to 300 K under zero external DC field for frequencies ranging from f=10 to 10,000 Hz. A prominent peak appears in both χ′ and χ″ as a function of T. The peak temperature T₂ of χ″ depends on f following the Vogel–Fulcher law. The particles show superparamagnetic behavior at room temperature, with transition to a blocked state at T_B^m94 K in ZFC and 119 K in AC susceptibility measurements, respectively, which depends on the applied field. The saturation magnetization and the coercivity measured at 4.2 K are 27.3 emu/g and 14.7 kOe, respectively. The particle size distribution was determined by fitting a magnetization curve obtained at 295 K assuming a log-normal size distribution. The interparticle interactions are found to influence the energy barriers yielding an enhancement of the estimated magnetic anisotropy, K=6×10⁶ erg/cm³. Mössbauer spectra obtained at higher temperatures show a gradual collapse of the magnetic hyperfine splitting typical for superparamagnetic relaxation. At 4.2 K, the Mössbauer spectrum was fitted with two magnetic subspectra with internal fields H_int of 490, 470 and 515 kOe, corresponding to Fe³⁺ ions in A and B sites.     

Temperature behavior of magnetization of DyCo2 compound

Zero field cooled (ZFC) and field cooled (FC) magnetization measurements were performed on the binary DyCo₂ cubic compound. Maxima for this compound were observed under ZFC magnetization. Below the broad maximum, irreversibility is observed. The magnetization curves for ZFC and FC regimes are split and magnetic moments for FC are higher than for ZFC. The dependence of the maxima upon the magnetic field and the time dependence of remanence is similar to the case of spin-glass-like systems.     

Implications of nanoparticle concentration and size distribution in the superparamagnetic behaviour of aging-improved maghemite xerogels

Evolution of static magnetic properties of a set of enhanced γ-Fe₂O₃/SiO₂ nanocomposites with different iron concentration has been studied on the basis of their corresponding hysteresis loops, zero-field/field-cooled (ZFC/FC) magnetization curves and transmission electron microscopy images. The lack of coercivity in all compositions, as well as the fulfillment of the H/T scaling law by the magnetization above the blocking temperature of each system under study, evidence a superparamagnetic behaviour in the iron oxide nanoparticles. In order to study the influence of iron content in the unblocking processes of nanoparticles, ZFC curves under different applied magnetic fields have been fitted to a model considering the systems under study as a distribution of energy barriers. Depart from the superparamagnetic model is discussed considering interparticle interactions.     

非均匀弱直流偏置磁场中CoFe-基非晶态合金丝的静磁化分布和退磁场分布

当前从事非晶态合金丝巨磁阻抗效应的理论研究均以忽略其内部退磁场为前提,该前提对于小尺寸非晶态合金丝不适用.本文提出一种用于计算Co Fe-基非晶态合金丝内部静磁化强度、退磁场分布的模型.该模型将非晶态合金丝内部划分成同轴、等宽、等厚、半径不同的相邻无交圆环,计算各圆环内磁化强度对场点r处退磁场冲激响应,得到冲激响应矩阵.利用该矩阵求解均匀/非均匀直流偏置磁场中非晶态合金丝内静磁化强度、退磁场分布.     

Phase distribution and computed magnetic properties of high-remanent composite magnets

Numerical micromagnetic calculations using finite-element techniques allow a quantitative treatment of the correlation between the microstructure and the basic magnetic properties of two-phase permanent magnets such as the remanence, the coercive field and the maximum energy product. For the investigation of (A) the role of the amount of the soft magnetic phase, and (B) the effect of grain shape, realistic three-dimensional grain arrangements have been used. The numerical results show that both short-range exchange and long-range magnetostatic interactions determine the magnetic properties. The optimal microstructure of an isotropic nanocrystalline permanent magnet was found to consist of soft magnetic particles with a large spontaneous magnetization embedded between hard magnetic grains. Exchange interactions than enhance the remanence of isotropic, composite magnets of Nd₂Fe₁₄B and -Fe by about 60%. Because of exchange hardening the soft magnetic phase can be increased up to 50% without a significant loss of coercivity. A uniform grain structure suppresses strong demagnetizing fields and this increases coercivity by 30% as compared with irregular shaped particles.     

Magnetic force microscopy investigation of the magnetization reversal of permalloy particles at high temperatures

The magnetization reversal of an array of permalloy particles formed by scanning probe lithography on the silicon dioxide surface has been investigated in the temperature range from room temperature to 800 K. Using scanning magnetic force microscopy and numerical calculations of the magnetic anisotropy field of a particle at different temperatures, it has been shown that an increase in the temperature leads to a decrease in the external magnetic field required to reverse the magnetization direction of the particle. From the obtained results, it has been concluded that the magnetization reversal of the studied particles is accompanied by the formation of an intermediate state with an inhomogeneous magnetization structure.     

Ferromagnetic properties of glucose coated Cu2O nanoparticles

Magnetic properties of glucose coated cuprous oxide nanoparticles of different sizes have been studied. Unlike bulk Cu₂O, which shows diamagnetic behavior, the nanoparticles show superparamagnetic behavior. A superparamagnetic blocking temperature of 21 K is observed for 5 nm particles. A magnetic hysteresis loop with a coercivity of 406 Oe is observed for these particles at 5 K. The magnetization and the coercivity increase with decreasing particle size. The superparamagnetic behavior, along with the increase in magnetization and coercivity with decreasing particle size, is due to the enhanced surface contributions to the magnetism.     

Locally frozen magnetic field in HTSC ceramics

The value of a locally frozen magnetic field in a region with a diameter of 0.5 mm in a 0.5-mm-thick YBa₂Cu₃O_{7 ? x} plate was investigated as a function of the excitation field (to 2 × 10⁴ Am^?1), plate cooling mode (in the absence or presence of a field; i.e., zero-field cooling (ZFC) or field coupling (FC)), and local demagnetizing field. Analysis of the measurement results in the noted range of excitation fields showed the following: (i) the dependence on the excitation field for the ZFC mode is explained by the local inhomogeneity of critical currents of weak links in the ceramic Josephson medium and is limited by their maximum value at the temperature of the experiment (77 K); (ii) the dependence on the excitation field for the FC mode contains a portion of the magnetic phase transition from the frozen current structure, typical of the initial portion of the dependence, to the current structure characteristic of the ZFC freezing mode, and is limited by this transition; and (iii) the dependence on the demagnetizing field for the ZFC mode can be explained by the stable coexistence (without annihilation) of microscopic current loops with opposite current directions in the ceramics.